EDB β€” 20F

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Definition 38

[20F] Let IβŠ‚β„, x0βˆˆβ„β€• accumulation point of I, f:I→ℝ function. We define

(1)lim supxβ†’x0f(x)=infUneighbourhood ofx0 supx∈U∩If(x)(2)lim infxβ†’x0f(x)=supUneighbourhood ofx0 infx∈U∩If(x)

where the first ”inf” (resp. the ”sup”) is performed with respect to the family of all the deleted neighbourhoods U of x0; and the neighbourhoods will be right or left neighbourhoods if the limit is from right or left.

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Book index
  • limsup, of function
  • liminf, of function
  • real numbers
  • liminf, of function
  • limsup, of function
  • function, liminf of β€” , see liminf
  • function, limsup of β€” , see limsup
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